Interval-valued Pythagorean fuzzy sets (IVPFSs) serve as a formidable tool for addressing uncertainty in information, resulting in their extensive adoption in the realm of decision making. The challenge of accurately measuring the similarity between IVPFSs remains a pressing issue. In this paper, we present some novel similarity measures based on trigonometric function and their weighted forms considering membership, non-membership and hesitancy degrees, respectively. These similarity measures adhere to key properties, which are demonstrated through numerical experiments. Subsequently, the proposed similarity measures tailored for IVPFSs are employed to address medical diagnosis and multicriteria decision-making (MCDM) problems within the context of interval-valued Pythagorean fuzzy environments. The results conclusively evidence that the proposed similarity measures result in substantially more efficient outcomes.
LiuZ. A new sine similarity measure based on evidence theory for conflict management. Commun Stat Theory Methods2025; 54: 3350–3366.
2.
MirghaderiSRoostaSBazyarA, et al.A fuzzy multi-criteria decision-making framework for constrained city gate station location selection problem in the natural gas network of Iran. Oper Res2025; 25: 84.
3.
de Andrés-SánchezJ. A systematic review of the interactions of fuzzy set theory and option pricing. Expert Syst Appl2023; 223: 119868.
4.
BesserisG. Non-linear saturated multi-objective pseudo-screening using support vector machine learning, pareto front, and belief functions: improving wastewater recycling quality. Appl Sci2024; 14: 9971.
5.
LiuZQiuHLetchmunanS, et al.Multi-view evidential c-means clustering with view-weight and feature-weight learning. Fuzzy Sets Syst2025; 498: 109135.
6.
EjegwaPAKausarNAgbaJA, et al.Determination of medical emergency via new intuitionistic fuzzy correlation measures based on spearman’s correlation coefficient. AIMS Math2024; 9: 15639–15670.
7.
LiXLiuZHanX, et al.An intuitionistic fuzzy version of hellinger distance measure and its application to decision-making process. Symmetry2023; 15: 500.
8.
EjegwaPAAnumMTIsifeKI. A new method of distance measure between intuitionistic fuzzy sets and its application in admission procedure. J Uncertain Syst2024; 17: 2440005.
9.
LiuZ. Fermatean fuzzy similarity measures based on Tanimoto and Sørensen coefficients with applications to pattern classification, medical diagnosis and clustering analysis. Eng Appl Artif Intell2024; 132: 107878.
10.
LiuZZhuSSenapatiT, et al.New distance measures of complex fermatean fuzzy sets with applications in decision making and clustering problems. Inf Sci (Ny)2025; 686: 121310.
11.
EjegwaPAOnyekeICKausarN, et al.A new partial correlation coefficient technique based on intuitionistic fuzzy information and its pattern recognition application. Int J Intell Syst2023; 2023: 5540085.
12.
LiuZHuangHLetchmunanS, et al.Adaptive weighted multi-view evidential clustering with feature preference. Knowl Based Syst2024; 294: 111770.
13.
RanH. A novel mabac approach for multi-attribute group decision-making with single-valued neutrosophic sets: an application in assessing microfinance group lending performance. Int J Knowledge-Based Intell Eng Syst2023; 27: 475–488.
14.
ZhengX. Intelligent framework for multiple-attribute decision-making under probabilistic neutrosophic sets and its applications. Int J Knowledge-Based Intell Eng Syst2023; 27: 503–513.
15.
LiuZ. An effective conflict management method based on belief similarity measure and entropy for multi-sensor data fusion. Artif Intell Rev2023; 56: 15495–15522.
16.
LyuSLiuZ. A belief Sharma-Mittal divergence with its application in multi-sensor information fusion. Comput Appl Math2024; 43: 34.
17.
NezamiMGitinavardHZadeAE. Soft computing-based new dynamic intuitionistic fuzzy group decision analysis for risk evaluation in BOT highway construction projects. Oper Res 2025; 25: 56.
18.
ZhuSLiuZ. Distance measures of picture fuzzy sets and interval-valued picture fuzzy sets with their applications. AIMS Math2023; 8: 29817–29848.
LiuYJiangW. A new distance measure of interval-valued intuitionistic fuzzy sets and its application in decision making. Soft comput2020; 24: 6987–7003.
26.
GohainBChutiaRDuttaP. A distance measure for optimistic viewpoint of the information in interval-valued intuitionistic fuzzy sets and its applications. Eng Appl Artif Intell2023; 119: 105747.
27.
DuKFanRWangY, et al.A data-driven group emergency decision-making method based on interval-valued intuitionistic hesitant fuzzy sets and its application in COVID-19 pandemic. Appl Soft Comput2023; 139: 110213.
28.
JiafuSWangDXuB, et al.An interval-valued intuitionistic fuzzy group decision-making method for evaluating online knowledge payment products. Appl Soft Comput2024; 150: 111046.
29.
NayagamVLGMuralikrishnanSSivaramanG. Multi-criteria decision-making method based on interval-valued intuitionistic fuzzy sets. Expert Syst Appl2011; 38: 1464–1467.
30.
DingHHuXTangX. Multiple-attribute group decision making for interval-valued intuitionistic fuzzy sets based on expert reliability and the evidential reasoning rule. Neural Comput Appl2020; 32: 5213–5234.
31.
SenapatiTChenGMesiarR, et al.Novel Aczel–Alsina operations-based interval-valued intuitionistic fuzzy aggregation operators and their applications in multiple attribute decision-making process. Int J Intell Syst2022; 37: 5059–5081.
32.
SalimianSMousaviSM. A multi-criteria decision-making model with interval-valued intuitionistic fuzzy sets for evaluating digital technology strategies in covid-19 pandemic under uncertainty. Arabian J Sci Eng2023; 48: 7005–7017.
33.
PengXYangY. Fundamental properties of interval-valued pythagorean fuzzy aggregation operators. Int J Intell Syst2016; 31: 444–487.
34.
GargH. A novel improved accuracy function for interval valued pythagorean fuzzy sets and its applications in the decision-making process. Int J Intell Syst2017; 32: 1247–1260.
35.
LiuYQinYHanY. Multiple criteria decision making with probabilities in interval-valued pythagorean fuzzy setting. Int J Fuzzy Syst2018; 20: 558–571.
36.
LiFXieJLinM. Interval-valued pythagorean fuzzy multi-criteria decision-making method based on the set pair analysis theory and choquet integral. Complex Intell Syst2023; 9: 51–63.
37.
AlhamziGJavaidSShuaibU, et al.Enhancing interval-valued pythagorean fuzzy decision-making through Dombi-based aggregation operators. Symmetry2023; 15: 765.
38.
LiLHaoM. Interval-valued pythagorean fuzzy entropy and its application to multi-criterion group decision-making. AIMS Math2024; 9: 12511–12528.
39.
EjegwaPA. New similarity measures for pythagorean fuzzy sets with applications. Int J Fuzzy Comput Modell2020; 3: 75–94.
40.
EjegwaPAOnyekeIC. Some new distance and similarity algorithms for pythagorean fuzzy sets with application in decision-making problems. In Handbook of research on advances and applications of fuzzy sets and logic, 2022, pp.192–211. IGI Global.
41.
HuangWZhangFWangS, et al.A novel knowledge-based similarity measure on intuitionistic fuzzy sets and its applications in pattern recognition. Expert Syst Appl2024; 249: 123835.
42.
AlreshidiNAShahZKhanMJ. Similarity and entropy measures for circular intuitionistic fuzzy sets. Eng Appl Artif Intell2024; 131: 107786.
43.
LiuZ. New tanimoto similarity measures between pythagorean fuzzy sets with applications on pattern recognition. In: Applied mathematics, modeling and computer simulation, 2023, pp.951–959. IOS Press.
44.
HussainZAlamSHussainR, et al.New similarity measure of pythagorean fuzzy sets based on the Jaccard index with its application to clustering. Ain Shams Eng J2024; 15: 102294.
45.
NguyenH. A novel similarity measure based on generalized score function for interval-valued intuitionistic fuzzy sets with applications. In: IEEE international conference on fuzzy systems, 2021, pp.1–8. IEEE.
46.
RathnasabapathyPPalanisamiD. A theoretical development of improved cosine similarity measure for interval valued intuitionistic fuzzy sets and its applications. J Ambient Intell Humaniz Comput2023; 14: 16575–16587.
47.
AlolyianHRazaqAAshfaqH, et al.Improving similarity measures for modeling real-world issues with interval-valued intuitionistic fuzzy sets. IEEE Access2024; 12: 10482–10496.
48.
LiHCaoYSuL, et al.An interval pythagorean fuzzy multi-criteria decision making method based on similarity measures and connection numbers. Information2019; 10: 80.
49.
PengXLiW. Algorithms for interval-valued pythagorean fuzzy sets in emergency decision making based on multiparametric similarity measures and WDBA. IEEE Access2019; 7: 7419–7441.
50.
BiswasASarkarB. Interval-valued pythagorean fuzzy todim approach through point operator-based similarity measures for multicriteria group decision making. Kybernetes2019; 48: 496–519.
51.
Al-BarakatiAMishraARMardaniA, et al.An extended interval-valued pythagorean fuzzy WASPAS method based on new similarity measures to evaluate the renewable energy sources. Appl Soft Comput2022; 120: 108689.
52.
MishraARPamučarDHezamIM, et al.Interval-valued pythagorean fuzzy similarity measure-based complex proportional assessment method for waste-to-energy technology selection. Processes2022; 10: 1015.
53.
AroraHDKumarVNaithaniA. Impact of trigonometric similarity measures for pythagorean fuzzy sets and their applications. Yugoslav J Oper Res2024; 34: 569–586.
54.
LiuZ. An evidential sine similarity measure for multisensor data fusion with its applications. Granular Comput2024; 9: 4.
55.
AliMY. Some trigonometric similarity measures of complex fuzzy sets with application. Ural Math J2023; 9: 18–28.
56.
LiuZLetchmunanS. An improved weighted evidence combination based on tangent similarity and its application in decision-making. Comput Decis Making Int J2024; 1: 38–50.
57.
XuZSChenJ. An overview of distance and similarity measures of intuitionistic fuzzy sets. Int J Uncertainty Fuzziness Knowledge-Based Syst2008; 16: 529–555.
58.
YeJ. Interval-valued intuitionistic fuzzy cosine similarity measures for multiple attribute decision-making. Int J Gen Syst2013; 42: 883–891.
59.
ZhangX. Multicriteria pythagorean fuzzy decision analysis: a hierarchical qualiflex approach with the closeness index-based ranking methods. Inf Sci (Ny)2016; 330: 104–124.
60.
WangZLiKWWangW. An approach to multiattribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weights. Inf Sci (Ny)2009; 179: 3026–3040.
61.
HatzimichailidisAGPapakostasGAKaburlasosVG. A novel distance measure of intuitionistic fuzzy sets and its application to pattern recognition problems. Int J Intell Syst2012; 27: 396–409.
62.
LuoMLiangJ. A novel similarity measure for interval-valued intuitionistic fuzzy sets and its applications. Symmetry2018; 10: 441.
